Worst hospital is involved in public dispute (9)
I believe the answer is:
overthrow
'worst' is the definition.
(both can mean to defeat)
'hospital is involved in public dispute' is the wordplay.
'hospital' becomes 'h' (abbreviation for hospital on maps).
'is involved in' indicates putting letters inside.
'public' becomes 'overt' (associated in meaning).
'dispute' becomes 'row' (row is a kind of dispute).
'overt'+'row'='overtrow'
'h' going inside 'overtrow' is 'OVERTHROW'.
(Other definitions for overthrow that I've seen before include "Ruin" , "Remove forcibly from power" , "destruction" , "Dethrone or oust" , "Trevor who? (anag)" .)